Formal pseudodifferential residue
= Formal pseudodifferential residue
{title2=$\operatorname{res}P=p_{-1}(x)$}
The formal residue is the <coefficient> of $\partial^{-1}$ after <coefficients> have been moved to the left by the <formal pseudodifferential composition rule>. It is not an analytic <residue> at a point. For scalar <coefficients>, the residue of a <commutator> is a total <derivative>; integrating it with vanishing boundary terms produces the cyclic <Adler trace>.